Dragoons: A Rotation Reborn

[SunnyHirose]

I suppose it won't be quite as satisfying as seeing the actual numbers or a more perfect equation, but it's still way, way better as an estimator as long as it reflects reasonable values and total DPS for current and near-current gear. Errors in auto-attacks... well, they're a smaller part of total damage.

I am a bit miffed as to the DET versus DET-202 issue, though. Having a term of .300 STR in the 58WD equation seems a little too perfect, somehow.

[Viridiana]

Dervy! Welcome back! Here, have those BLM numbers I've been promising! Alas, due to limited gear sets I wasn't able to get my Determination very high like you were asking.

51 WD, 493 INT, 294 Determination 50 potency (Blizzard II)
Non-critical 98-109, critical 148-163

51 WD, 493 INT, 294 Determination 100 potency (Fire II)
Non-critical 198-219, critical 298-327

51 WD, 329 INT, 324 Determination 50 potency
Non-critical 70-77, critical 104-115

51 WD, 329 INT, 324 Determination 100 potency
Non-critical 141-156, critical 211-233

And a "full gear" set:
66 WD, 508 INT, 301 Determination 50 potency
Non-critical 123-136, critical 185-204

66 WD, 508 INT, 301 Determination 100 potency
Non-critical 245-270, critical 367-406


So, umm. . .why are the 100 potency numbers not 2x the 50 potency ones? >_> I could understand 2x+1 due to rounding, but the crit values on the second set are 2x+3. . . and then the third set are actually less than 2x the originals. I'd like to think that the 50 potency crits on the third set are supposed to be 184-204, but the game refuses to give me a 184 crit despite hundreds of crits. . .so yeah.

[SunnyHirose]

Astral Fire is a damage buff, Umbral Ice is not.

[Viridiana]

Astral Fire and Umbral Ice are damage buffs as well as MP thingummies.

Yeah, I should have been clear. The Blizzard II was all done either unbuffed or with only Umbral Ice stacks (which don't boost Ice damage); and the Fire II casts were interwoven with Blizzard casts to remove the Astral Fire buff. Blizzard III when almost out of MP, then Fire I to remove the UI3 stack, back into Fire II (which is why I was lucky to get the extremes as quickly as I did, takes forever to weave like that).

[Dervy]

numbers

Thanks! This'll help a lot

By the way, Sunny, when I go and start looking into Job Coefficients, how should I determine what is "*1", as in, no affect on the base-line of damage? The JP's, if I'm not mistaken, measured the Baseline to be of a Marauder (*1) and scaled all of the other jobs around this. Should I do something similar, or should I identify the Job with the lowest impact on Damage, then use a coefficient to scale up the damage of the others?

[SunnyHirose]

Yeah, I should have been clear. The Blizzard II was all done either unbuffed or with only Umbral Ice stacks (which don't boost Ice damage); and the Fire II casts were interwoven with Blizzard casts to remove the Astral Fire buff. Blizzard III when almost out of MP, then Fire I to remove the UI3 stack, back into Fire II (which is why I was lucky to get the extremes as quickly as I did, takes forever to weave like that).

Okay, so let's say this is what happens internally (not necessarily right--there's a good chance values are rounded down instead of nearest--but it is something like this):

round((magic number) * (±5% variation) * (buff multipliers) * potency * (1.5 if crit 1 if not))

Let's try finding this magic number for 66 WD, 508 INT, 301 DET. Due to the rounding, a raw damage amount could be ±0.5 off this way. So, 123 could imply that the value before rounding was anywhere from 122.5 to 123.5. The corresponding critical hit value 185 could be anywhere from 184.5 to 185.5, or 123 to 123.666667. In practice, I don't really assume I have the minimum/maximum crit values unless their scaled values really are the lowest (it takes too long compared to just using different skills/buffs), but since you're pretty sure here, it's not unreasonable to conclude that the 123 value is most likely rounded down from something and you're not going to see a 184 crit (-> 122.333333~123).

On the 100 potency data, you can do similar calculations to find that 367 (-> 244.333333-245) demonstrates a lower crit-adjusted value than 245 (-> 244.5 - 245.5). Or yea, even lower than the 50 potency value we were just looking at (-> 245-247).

So, does this mean we have two almost mutually exclusive ranges for minimum value and this game is buuuuusted? Well, maybe not, but it's exactly why I've been complaining about the rounding for a while. For example, we don't really know how that ±5% thing works, we just know that's roughly what it does. We really don't know about what floating-point or fixed-point madness may be lurking in the background, or about any rounding that may happen before what we could presume to be a final rounding. Anyhoo we came for an estimate of the "magic number", and that's what we're gonna do first.

204 / 1.5 = 136 = 136 -> 271.333334-272.666667
406 / 1.5 = 270.666667 > 270 -> 270.333333-271

100 potency value here is lower again. But being more damage, the values are more accurate (in fact, I simply don't). What I've been personally doing is going "okay, the lowest attested value is 244.666667 and the highest is 272", which gives us a midpoint of 258.333333, which I do because I'm not sure where to go from there. But surely the ranges that could be rounded from could tell us more?

What I can tell you is this is how it translates:
258.333333 * .95 * .5 * 1 = 122.708333 => 123
258.333333 * .95 * .5 * 1.5 = 184.0625 => 184
258.333333 * 1.05 * .5 * 1 = 135.62500 => 136
258.333333 * 1.05 * .5 * 1.5 = 203.4375 => 203
258.333333 * .95 * 1 * 1 = 245.416666 => 245
258.333333 * .95 * 1 * 1.5 = 368.12500 => 368
258.333333 * 1.05 * 1 * 1 = 271.25 => 271
258.333333 * 1.05 * 1 * 1.5 = 406.874999 => 407

And for the most part, I run into this trouble most with attacks that have the lowest expected values; it seems to settle down a little though not completely when the hits are harder.

tl;dr lowpotencies nobuffs data arrrrgh

Thanks! This'll help a lot

By the way, Sunny, when I go and start looking into Job Coefficients, how should I determine what is "*1", as in, no affect on the base-line of damage? The JP's, if I'm not mistaken, measured the Baseline to be of a Marauder (*1) and scaled all of the other jobs around this. Should I do something similar, or should I identify the Job with the lowest impact on Damage, then use a coefficient to scale up the damage of the others?

DRG is #1!

It doesn't really matter. I feel players would be better serviced by having separate equations instead of a grand unifying one.

[Viridiana]

tl;dr lowpotencies nobuffs data arrrrgh

Yeah, it's frustrating. Taking, for example, this row of yours:

258.333333 * .95 * 1 * 1.5 = 368.12500 => 368

It's problematic, because according to the math there, the lowest crit should be 368. But theres a 367 observed crit. So, plugging in the highest value that could round down to 367, we get:

X * .95 * 1 * 1.5 = 367.4999999 => 367
X * .95 = 249.9999999 => 250
X = 257.894736

So, X can't be bigger than that, or we don't see the 367 crit that I saw. But, then, step two of that shows that 257.894736 *.95 only drops to 250, and woudn't show the 245 non-crit I observed.

X * .95 * 1 * 1 = 244.5 => 245 is the lowest value that would allow a 245 non-crit
X = 257.368421 is the lowest X value for a 245 non-crit

X * .95 = 245.4999999 => 245 is the highest value allowing a 245 non-crit
X = 258.421052 is the highest X value

Going back to the critical value. . .

X * .95 * 1.5 = 366.5 => 367 is the lowest value that yields 367
X * .95 = 244.3333333 => 244 (which we know is too low, but hey)
X = 257.192928

So, the actual X value to observe the minimums I have is between 257.368421 and 257.894736. This is the range for the minimums. Let's do the maximums.

269.5 < X * 1.05 < 270.4999999
256.666666 < X < 257.619047 Progress, because this upper bound is smaller than the old one.

405.5 < X * 1.05 * 1.5 < 406.4999999
257.460317 < X < 258.095238 And now we have a better lower bound, too. . .

257.460317 < X < 257.619047 These are the boundaries for 100 potency. For 50 potency. . .

Minimums:

122.5 < X * .95 * .5 < 123.4999999
257.894736 < X < 259.999999 Which is out of our boundary for 100 potency. . .

184.5 < X * .95 * .5 * 1.5 < 185.4999999
258.947368 < X < 260.350877

So, 258.947368 < X < 259.999999 for the minimums

Maximums:

135.5 < X * 1.05 * .5 < 136.4999999
258.095238 < X < 259.999999

203.5 < X * 1.05 * .5 * 1.5 < 204.4999999
258.412698 < X < 259.682539

So, the boundaries are:

100 Potency: 257.460317 < X < 257.619047
50 Potency: 258.947368 < X < 259.682539

And there is no overlap between the bounds

[pandabearcat]

Are you guys even sure the construction of your formula is correct?

[Divine_Intervention]

Came to see some information on how to use dragoon properly. What i got was a headache and a math class lol.

[SunnyHirose]

Are you guys even sure the construction of your formula is correct?

Well, I mean, if you followed that whole chain... we have conclusively demonstrated that it isn't.